In conventional gas bag modules having a mounting part, tethers or the gas bag itself must be fastened very securely and hence in a costly manner to the mounting part, so that they are not detached from their anchoring on activation of the gas bag module, in which process they are stressed in a tensile manner. This detachment from the anchoring can take place for example by a tearing out of the piece of fabric, i.e. of the tether or of the gas bag.